Question

Suppose that you have received 100 email messages 90 of which are genuine and
10 are spam. Suppose that your email server runs a spam filtering software that
classified the above email messages as follows.
• Out of the the 90 genuine messages 88 classified as genuine but 2 are wrongly
flagged as spam.
• The probability of correct classification of a message is at least 97%
Using the above data, please answer the three questions below. Each answer must
be accompanied with an explanation as to why you believe the answer to be correct.
A correct answer only (without the explanation) will be worth 1 point for part a),
2 points for part b), and 2 points for part c). Explanation only without an explicit
answer will not be awarded any marks.

(a)	What is largest possible number of spam messages (out of 10) that the software
can incorrectly classify as genuine?	.
(b)	What is the smallest possible probability that the spam filter flags an email
message as spam provided that the message is indeed a spam?
(c)	What is the smallest probability that an email message is spam provided that
it is flagged as spam by the spam filter?	(8 marks

Answer 1

Solution:

a) Considering the lowest probability of correct classification be 97%, so out of 100 messages at max 3 can be classified as wrong, and already out of the 90 genuine messages two are wrongly classified, so only 1 can be classified inaccurately for spam messages, meaning 1 out of the 10. So the largest number of spam messages that can be incorrectly classify as genuine is 1.

b) Smalles probability of reading the spam as spam, means highest probability of making a mistake with the spam emails, that is 1/10 = 10% chance of being wrong, while 90% chance of guessing the spam as indeed a spam.

c) The system flagged 2 correct messages as spam as well, and 9 spam messages as spam, so smallest probability will be = 9/11 = 0.81818 = 81.82% Answer